Carbon nanotube excitation system

ABSTRACT

A carbon nanotube excitation system is disclosed. The excitation system is suitable to vibrate the nanotube and to excite at least one nanotube resonant frequency. Types of excitation systems include but are not limited to electromagnetic system having a coil or an antenna, mechanical system having piezoelectric elements, electrostatic system having capacitive element, electromagnetic system having a magnetic element, and electrostatic system having charged nanotube.

CROSS-REFERENCE TO RELATED APPLICATION

Under 35 U.S.C. §120, this application claims the benefit of commonlyowned U.S. patent application Ser. No. 09/881,650 entitled SYSTEM ANDMETHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR ATOMIC FORCE MICROSCOPY,by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Jun.13, 2001, which is also hereby incorporated by reference.

In addition, under 35 U.S.C. §120, this application claims the benefitof commonly owned U.S. patent application Ser. No. 09/499,101 entitledSYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR ATOMIC FORCEMICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure,filed on Feb. 4, 2000, which is also hereby incorporated by reference.

Additionally, via U.S. patent application Ser. No. 09/499,101, and under35 U.S.C. §119(e) and 120 and 37 C.F.R. §1.53(b), this applicationfurther claims the benefit of commonly owned U.S. Provisional PatentApplication No. 60/118,756 entitled MULTI-DIMENSIONAL FORCE SENSINGSYSTEM FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, DavorJuricic, and Paul F. McClure, filed on Feb. 5, 1999, which is alsohereby incorporated by reference.

This application also incorporates by reference commonly owned U.S.patent application Ser. No. 09/404,880 entitled MULTI-DIMENSIONALSENSING SYSTEM FOR ATOM FORCE MICROSCOPY, by Vladimir Mancevski,hereinafter referred to as “MANCEVSKI1.”

Furthermore, this application also incorporates by reference commonlyowned issued U.S. Pat. No. 6,146,227 entitled METHOD FOR MANUFACTURINGCARBON NANOTUBES AS FUNCTIONAL ELEMENTS OF MEMS DEVICES, by VladimirMancevski, hereinafter “MANCEVSKI2.”

TECHNICAL FIELD OF THE INVENTION

The present invention relates generally to the field of forcemeasurement using scanning probe microscopy (SPM) and, moreparticularly, to a force measurement system for determining thetopography or composition of a local region of interest by means ofscanning probe microscopy.

BACKGROUND OF THE INVENTION

Introduction of Terms used in this Disclosure

In this invention we use Cartesian coordinate systems with perpendicularaxes as the coordinate system of choice. Nevertheless, one may implementany other well-defined coordinate system including, for example, polar,cylindrical, or spherical coordinate system. The “global” coordinatesystem X Y Z 40 is fixed with the sample and the “local” coordinatesystem X_(tip) Y_(tip) Z_(tip) 42 is fixed with the apex 45 of the tip44 of the scanning probe 48. In general, the scanning probe tip apex 45may have an arbitrary position and orientation with respect to thesample, therefore, the local coordinate system 42 also may havearbitrary position and orientation with respect to the global coordinatesystem 40, as shown in FIG. 1A. In a special case, the local 42 andglobal 40 coordinate systems may be aligned with respect to one another,as shown in FIG. 1B.

The origin of the local coordinate system 42 is at the apex 45 of thetip 44. The Z_(tip) axis 46 is oriented along the length of the tip 44and is perpendicular to a region of the oscillator 48 surface near theplace where the tip 44 is attached The X_(tip) axis 50 is parallel tothe long axis of the oscillator 48. The Y_(tip) axis 52 is transversewith respect to the X_(tip) axis 50 so as to form a right-handedCartesian coordinate system.

It is known that a dipole-dipole interaction occurs between pairs ofatoms located in volumetric regions of the tip 44 and sample 54 whenthey are in proximity to each other. The associated force is called Vander Walls force. The resulting integrated effect encompasses alldipole-dipole interactions between pairs of atoms in sufficientproximity to generate a measurable interaction between the tip 44 andthe sample 54. This resultant of the integrated dipole-dipoleinteraction is represented by a three-dimensional “tip-sampleinteraction force vector” 56 as shown in FIG. 2A. A single point can beused to approximate the volumetric region near the tip apex 45, and aflat surface can be used to approximate the region of the sample 54 inproximity to the tip 44, as shown in FIG. 2B. If the surface of thesample 54 is horizontal (i.e., in the XY plane) the tip-sampleinteraction force vector 56 will be vertical. However, if the surface ofthe sample 54 is vertical (e.g., in the XZ plane) the tip-sampleinteraction force vector 56 will be horizontal. For a generalorientation of the surface of the sample 54, the tip-sample interactionforce vector 56 will have three non-zero components, corresponding tothe three axes XYZ of the global coordinate system 40. The tip-sampleinteraction force vector F 56 can be represented either by itscomponents F_(x tip), F_(y tip), F_(z tip) in the local coordinatesystem 42 or by its components F_(X), F_(Y), F_(Z), in the globalcoordinate system 40.

In one possible mathematical representation, the 3×1 vector functionsΦ_(i), for (i=1, 2, 3, . . . ∞), of the spatial coordinates (e.g.,X_(tip) Y_(tip) Z_(tip)) represent mode shapes of the probe structure,and q_(i) represent the corresponding generalized coordinates. In oneinstance of a classical modal analysis, the equations of motion of theprobe areM _(j) d ² q _(j) /dt ² M _(j) ω² q _(j) −Σ _(i=1 to ∞) F _(ij) ′q _(i)=F _(0j)Where (j=1, 2, 3, . . . ∞), M_(j) is the modal mass, ω_(j) is theresonant frequency, and F_(oj) is the static component of thegeneralized force corresponding to the tip-sample interaction forceapplied to the probe tip. The term—Σ_(i=1 to ∞)F_(ij)′ q_(i) can beinterpreted as a negative spring force which alters the j^(th) resonantfrequency of the vibrating probe. The quantity F_(ij)′ can berepresented in terms of the mode shapes byF _(ij) ′=[A]Φ _(i)(tip)·Φ_(j)(tip).Where [A] is a 3×3 coefficient matrix arising from classical modalanalysis and the symbol · denotes an inner product of two vectors.

The vector [A] Φ_(i)(tip), derived from classical modal analysis, is anexample of a more general vector quantity that we call a “resultantsurface force interaction.” Our use of the term “resultant surface forceinteraction” is not limited to any particular physical origin of thetip-sample interaction force and may include, for example, bothconservative and non-conservative tip-sample interaction forces.

FIG. 3A shows typical orientations of three selected mode shape vectors,evaluated at spatial coordinates corresponding to the apex 45 of a probetip 44. In this example, Φ₁ (tip) 58 represents the direction in whichthe tip apex 45 moves when the main bending mode is excited, Φ₂(tip) 60represents the direction in which the tip apex 45 moves when the firsttorsional mode is excited and Φ₃(tip) 62 represents the direction inwhich the tip apex 45 moves when the second bending mode is excited. Fora suitably chosen structural design of the probe 48 and tip apex 45location, and for small-amplitude vibrations, Φ₃(tip) 62, Φ₂(tip) 60 andΦ₁ (tip) 58 are each substantially aligned with the unit vectors,i_(tip) 64, j_(tip) 66, and k_(tip) 68, respectively, and the modalcoordinates q₃, q₂, q₁ can be approximated by tip 44 displacements alongthe in the X_(tip) 50 Y_(tip) 52 Z_(tip) 46 axes respectively. In thisexample the resultants of the surface force interaction can be given ageometric interpretation as vectors aligned along the X_(tip) 50 Y_(tip)52 Z_(tip) 46 axes.

The resultant surface force interaction vectors F′_(x tip) 70,F′_(y tip) 72 and F′_(z tip) 74 can, in some cases, be modeled by thethree virtual springs with variable spring constants k₁ 76, k₂ 78, andk₃ 80 that are functions of the tip-surface distance, as shown in FIG.3B. The vector F′ 82 shown in FIG. 3C is the sum of the three resultantsurface force interaction vectors. As the force axis 84 and the distanceaxis 86 show in FIGS. 4A and 4B, the force-distance curve 88 shows thatthe resultant surface force is non-linear with respect to thetip-surface distance. Therefore, the modeled spring constants are alsonon-linear. However, for small amplitudes of vibration of the oscillatortip 44, the spring constants are linear with respect to the tip-surfacedistance. To maintain linear response, the oscillator 48 should vibratewith sufficiently small amplitude to keep the oscillator in a linearregime of operation, shown by area of measurement 90. Contrast that witharea of measurement 92, used in tapping mode. Force axis 84 showsrepulsive force 94 and attractive force 96.

The term “oscillator,” as used in conjunction with the presentinvention, represents a scanning probe 48 for which multiple resonantmodes are intended to be used for force sensing. The term “cantilever”refers to a scanning probe 48 for which only the primary bending (i.e.,“cantilever”) mode is intended to be used for force sensing, eventhough, in general, the probe 48 structure would exhibit multipleresonant modal responses if excited at the appropriate drivingfrequencies.

The term “force sensor” refers to the resonating oscillator 48 and itssensitivity to surface forces 82 associated with the tip-sampleinteractions. The purpose of the force sensor is to enable detection ofthe surface topology or composition by means of coupling the scanningprobe tip 44 to the surface of the sample 54 via a tip-sampleinteraction force 82. In general, the interaction force 82 between thetip 44 and the sample 54 is a non-linear function of the tip-surface gapthat includes the dipole-dipole interaction described above (which isconservative and hence describable by a potential), plus additionalcontributions from other conservative forces (e.g. electrostatic andmagnetic forces) and non-conservative forces (e.g., meniscus forces andother forces due to surface contamination). However, whatever its originin terms of atomic interactions, molecular interactions or other surfacephysics phenomena, the tip-sample interaction force vector 56 can stillbe represented by a vector composed of three generally non-zerocomponents, corresponding to the three axes XYZ of the global coordinatesystem 40. Alternatively, the tip-sample interaction force 82 can berepresented by a vector 56 composed of three generally non-zerocomponents, corresponding to the three axes X_(tip) Y_(tip) Z_(tip) ofthe local coordinate system 42. Equal and opposite tip-sampleinteraction forces 82 act on the tip 44 and sample 54, respectively,consistent with Newton's law of action and reaction.

“Force sensing” occurs when the surface force interaction alters theeffective elastic restoring force associated with one or more resonantmodes of the primary probe 48 structure so as to shift the respectivenatural frequencies of its resonant modes. The shifts in naturalfrequency can be sensed, for example, by monitoring either theamplitudes or phases of the respective modal oscillations.

When using the term “at” in the claims herein to describe a positionalrelationship between two objects, the term “at” is intended to beinterpreted as meaning: (i) contacting the surface 54 or (ii) locatednear to but not contacting the surface 54. For example, when a SPM tip44 is “at” a sample surface 54 during a scan, the tip 44 may becontacting the surface 54 (as in contact or tapping mode testing), orthe tip 44 may be located near to the surface 54 but without contactingthe surface 54 (as in non-contact testing). As another example, when adistal end of a nanotube is “at” a surface 54 of a semiconductorintegrated circuit, the distal end of the nanotube may be contacting ortapping the surface 54, or the distal end of the nanotube may be locatednear the surface 54 without contacting the surface 54.

BACKGROUND OF THE RELATED ART

A scanning probe typically consists of a primary probe structure 48,(which may be either an oscillator or a cantilever) and a highaspect-ratio, sharply-pointed tip 44 extending from its end. The tip 44is generally much less massive than the primary probe structure 48. Thefunction of the primary probe structure is to provide one resonant mode(in the case of a cantilever) or more than one resonant mode (in thecase of an oscillator), which are utilized for force sensing. Typically,the primary probe structure 48 is about 100 microns long by 30 micronswide by 2 microns thick. The function of the tip 44 is to rigidly couplethe primary probe structure 48 to a relatively small volumetric region(the tip apex 45) which can be positioned so as to interact with arelatively small region of the sample 54 in proximity to the tip apex45. Typically, the tip 44 is an inverted cone or a pyramid with its apex45 pointing towards the sample surface 54. Ideally, the apex 45 of thetip 44 would be a single atom that couples with the sample surface 54via the tip-sample force interaction. In reality, the apex 45 of the tip44 typically has a radius of about 10 nanometers, and the cone-shaped orpyramid-shaped tip 44 is typically a few microns long.

In conventional scanning probe microscopy (SPM), the force sensor isonly sensitive to the resultant of the surface force interactionF′_(z tip) 74, in the Z_(tip) 46, direction, as illustrated in FIGS. 5Aand 5B. The other two components of the surface force interactionvector, F′_(X tip) 70 in X_(tip) 50 direction and F′_(Y tip) 72 in theY_(tip) 52 direction, are not detected in conventional scanning probemicroscopy. The XYZ and X_(tip) Y_(tip) Z_(tip) coordinate systems areshown in FIGS. 5A and 5B as being aligned for ease of illustration. Forconventional non-contact mode scanning, a SPM cantilever 48 is excitedin its first bending mode with small amplitude, thereby causing the tip44 to move within the attractive region of the surface force interactionprofile. This region 90 is illustrated in FIG. 4A. In the conventional“tapping” mode, the amplitude of the cantilever 48 vibration is largerand the tip 44 dips in and out of both the attractive 96 and repulsive94 regions of the surface force interaction region 92, as shown in FIG.4B. A change in the tip-surface distance during the scanning processshifts the cantilever 48 resonance. A feedback loop uses the resonanceshift to maintain either the amplitude or phase of the oscillation at apredetermined value. The output from the resulting scan is used torepresent the topography or composition of the surface. Scanning of theprobe in an XY raster plane while recording the response of the forcesensor in Z direction can be used to construct a three-dimensionalprofile of the surface 54.

There are two major consequences of the failure of conventional SPMs todetect the surface force interaction in multiple directions: (1) thevertical and horizontal distance scales will be different due to adiminished projection of the surface force interaction vector onto thevertical axis when the sample surface is not horizontal, and (2) therewill be loss of force sensor sensitivity over highly sloped samplesurfaces. To illustrate these points, we examine a tip 44 that isoriented in the Z direction as it scans in the Y direction over ahorizontal surface 54 in the XY plane, as shown in FIG. 6. In thisscenario, the surface force interaction 82 will be in the Z directionwhen the surface 54 is horizontal. A conventional force sensor woulddrive the tip 44 at a constant surface force interaction set forscanning the horizontal surface. If the slope of the surface 54 changes,and with that the direction of the surface force interaction vector 82,the conventional force sensor would still only respond to the surfaceforce interaction in the Z direction 74. However, for a tilted surface,the surface force interaction in the Z direction 74 is diminished by afactor equal to the cosine of the surface 54 slope angle representingthe loss of the horizontal component 72 of the surface force interactionvector 82. The feedback controller of the conventional force sensorwould keep the tip 44 over the sloped surface 54 at a constant surfaceforce interaction level set for the horizontal surface 54. Thismisrepresentation will cause the tip 44 to be closer to a sloped surface54 than to a horizontal surface 54, causing a distortion of thehorizontal and vertical distance scales and a distortion of the surface54 topography. This unwanted approach of the tip 44 to the surface 54may also cause snapping of the tip to the surface. This snapping maydamage the tip 44 or the sample 54.

Naturally, this problem is more emphasized when the surface is close tovertical or is vertical. For the case of a vertical surface, the surfaceforce interaction occurs only in the horizontal direction. However, theconventional force sensor is only sensitive to a surface forceinteraction in the vertical direction. Therefore, the conventional forcesensor loses its sensitivity over highly sloped surfaces and would notwork for vertical or close to vertical surfaces.

One prior art embodiment, shown in FIG. 7, operates in a non-contactmode and has a cantilever 48 that resonates in the Z direction anddithers (a non-resonant vibration) in the Y direction. This approach issufficient to enable force sensitivity in two directions. However, theforce sensitivity in the lateral direction is not as good as the forcesensitivity in the vertical direction. This is due to the use ofdithering in the Y direction rather than use of a distinct resonant modethat can provide higher force sensitivity. If the sample surface 54 isvertical, the vertical surface force interaction vanishes completelywhich renders the dithering approach ineffective.

Therefore it would be desirable to operate a force sensor that providesforce sensitivity in all three directions by means of distinct resonantmodes.

All references cited herein are incorporated by reference to the maximumextent allowable by law. To the extent a reference may not be fullyincorporated herein, it is incorporated by reference for backgroundpurposes, and indicative of the knowledge of one of ordinary skill inthe art.

BRIEF SUMMARY OF THE INVENTION

The problems and needs outlined above are addressed by the presentinvention. In accordance with one aspect of the present invention, ascanning probe microscopy (SPM) tool is provided. The SPM tool comprisesan oscillator, an SPM tip, a mechanical actuator, a sensing system, anda feedback control system. The oscillator having the SPM tip extendingtherefrom. The mechanical actuator is adapted to hold the oscillator andposition the SPM tip relative to a sample. The oscillator has a selectedshape, dimensions ratio, and/or material composition such that theoscillator comprises a first resonant mode for a first direction,wherein a first resonance of the first resonant mode can be altered by asurface force interaction between the SPM tip and the sample in thefirst direction; and a second resonant mode for a second direction,wherein a second resonance of the second resonant mode can be altered bythe surface force interaction between the SPM tip and the sample in thesecond direction. The sensing system is adapted to sense the alterationsin the first and second resonances, is adapted to provide a first outputbased on the alterations in the first resonance, and is adapted toprovide a second output based on the alterations in the secondresonance. The feedback control system is adapted to control theactuator based on the first and second outputs. Nanotubes can be grownfrom the tip to provide more advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages of the invention will become apparent uponreading the following detailed description and upon referencing theaccompanying drawings, in which:

FIG. 1A shows a scanning probe tip with an arbitrary position andorientation with respect to a global coordinate system;

FIG. 1B shows a special case of FIG. 1A in which the local and globalcoordinate systems have the same orientation with respect to oneanother;

FIG. 2A shows the tip-sample interaction force vector as the resultantof the integrated dipole-dipole interaction;

FIG. 2B shows a single point used to approximate the volumetric regionnear the tip apex, and shows a flat surface used to approximate theregion of the sample in proximity to the tip apex;

FIG. 3A shows typical orientations of three selected mode shape vectors,evaluated at spatial coordinates corresponding to the apex of a probetip;

FIG. 3B shows the resultant surface force interaction vectors modeled bythe three virtual springs with variable spring constants that arefunctions of the tip-surface distance;

FIG. 3C shows a vector which is the sum of three surface forceinteraction vectors;

FIGS. 4A and 4B show the resultant surface force as a non-linearfunction with respect to the tip-surface distance;

FIGS. 5A and 5B show that in conventional scanning probe microscopy(SPM), the force sensor is only sensitive to the resultant of thesurface force interaction in the direction (Z_(tip)) along the length ofthe tip;

FIG. 6 shows scale error that occurs when a tip of a conventional SPMthat is oriented in the Z direction scans over a sloped surface;

FIG. 7 shows a prior art embodiment having a cantilever that resonatesin the Z_(tip) direction and dithers (a non-resonant vibration) in theY_(tip) direction;

FIG. 8 shows the first bending mode which generates tip vibration in thedirection along the length of the tip;

FIG. 9 shows the first torsional mode which generates tip vibration inthe direction transverse to the long axis of the oscillator;

FIG. 10 shows the second bending mode which generates tip vibration inthe direction along the long axis of the oscillator;

FIG. 11 shows a scanning probe tip located at a node of a mode shape;

FIG. 12 shows another embodiment of the present innovation that utilizespaddle-shaped oscillator made of single crystal silicon;

FIG. 13 shows another embodiment of the present innovation that utilizesnotched diving-board shaped oscillator;

FIGS. 14 and 15 show alterations of multiple resonances in response totip-surface interactions in multiple directions. FIGS. 14 and 15 alsoshow the directions of tip motion for the first bending and firsttorsional modes of the oscillator;

FIG. 16 shows an embodiment of the present invention where theoscillator is tilted around the long axis of the oscillator to provideaccess to a feature with reentrant sidewall;

FIG. 17 shows a SPM tip reaching vertical and reentrant sidewallsurfaces of a sample with periodic dense high-aspect-ratio features;

FIG. 18 shows an experimentally obtained scan of a line in asemiconductor integrated circuit with the tilted probe system;

FIG. 19 shows an embodiment of the present invention in which standardoscillator tip is extended with an aligned nanotube tip grown from theapex of the sharp tip using the method of MANCEVSKI2;

FIG. 20 shows an embodiment of the present invention with a supportstructure on which carbon nanotube tip extensions are oriented inlateral and vertical directions as to enable imaging of vertical andnear vertical sidewalls and trench bottoms; carbon nanotube tipextensions may also function as nanotube oscillators;

FIG. 21 shows three possible resonant modes of a carbon nanotubeoscillator;

FIG. 22 shows a magnetic particle attached at the end of the nanotube soas to destroy the symmetry and produce distinct resonances withseparated modes; the magnetic particle may also be used to magneticallyexcite the nanotube oscillator;

FIG. 23 shows the spatial domain based method of vibration sensing; and

FIG. 24 shows an embodiment of the present invention where the tip scanslongitudinally along features instead of laterally with respect to suchfeatures.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout the various views,embodiments of the present invention are illustrated and described, andother possible embodiments of the present invention are described. Thefigures are not necessarily drawn to scale, and in some instances thedrawings have been exaggerated and/or simplified in places forillustrative purposes only. One of ordinary skill in the art willappreciate the many possible applications and variations of the presentinvention based on the following examples of possible embodiments of thepresent invention.

System and Method for Force Sensing with Sensitivity in MultipleDirections

The system and method for force sensing of the present invention relieson the use of at least two separate oscillator resonant modes to becomesensitive in at least two directions (preferably Y_(tip) and Z_(tip)),where the modal shape of the oscillator 48 and the location of the tipapex 45 determine the directions of the force sensor sensitivity. Theshape, dimensions ratio, and/or material composition can be varied tochange the direction of tip-surface force interaction sensitivity for agiven natural frequency of the oscillator 48.

An embodiment of the present invention relies on the use of at least twoseparate oscillator resonant modes to become sensitive in at least two(preferably Y_(tip) 52 and Z_(tip) 46) directions.

A particular resonant shape and particular tip apex 45 location in aproximity to a three-dimensional surface 54 can provide a surface forceinteraction that will act only in the direction of the tip vibrationaltering the given resonance. For that particular resonant mode, theactual surface force interaction will not produce any work in any otheraxis but the axis of the vibration of the tip 44. Hence, the shape,dimensions ratio, and/or material composition of an oscillator 48 and/orthe location of the probe tip 48, can be selected or designed so thatthe SPM probe is sensitive to predetermined directions or components ofthe tip-sample force interaction vector 56.

Preferably, an embodiment of the present invention can rely on the useof three separate oscillator resonant modes to become sensitive in threedirections (or each axis of a Cartesian coordinate system), where themodal shape of the oscillator 48 shape and dimensions ratio), thematerial composition of the oscillator 48, and/or the location where thetip 44 portion extends from the oscillator 48 determine these directions(or axis).

Ideally, each oscillator resonant mode corresponds to a single directionof the force sensor sensitivity. However, each oscillator resonant modemay correspond to multiple (two or three) directions of the force sensorsensitivity. Preferably, the three directions are different from eachother. Preferably, the three directions are perpendicular to each other.

Preferably, the three perpendicular directions are aligned with theX_(tip) 50, Y_(tip) 52, and Z_(tip) 46 axes of the oscillator. Themultiple directions (two or more) need not be perpendicular to eachother. However, a choice of utilizing substantial perpendiculardirections can allow transformations and calculations to be made mucheasier and faster.

For a given relative position and orientation between the localcoordinate system 42 of the scanning probe 48 and a global coordinatesystem 40 of the sample surface 54 we can transform the directions ofthe force sensor sensitivity to any coordinate system of choice.Preferably, the coordinate system of choice is the global coordinatesystem 40 of the sample 54.

Advantages of the Present Invention

The present invention provides a force sensor that addresses thelimitations of the conventional force sensors described in thebackground section of this disclosure. Described below are some of theadvantages currently realized by the present invention, and there may bemore advantages that will be later realized but are not described.

The force sensor of the present invention provides an importanttechnical advantage by providing sensitivity to variations in resonantvibrations in two or more directions, in contrast to a conventionalforce sensor that is only sensitive to variations in resonant vibrationsin one direction. Also, the present invention provides the ability to besensitive to surface force interactions along three distinct axis (e.g.XYZ of a Cartesian coordinate system), which provides the ability toperform three-dimensional, high-sensitivity scans to detect the contoursof complex three-dimensional surfaces 54.

The advantage of the force sensor of the present invention is that itcan determine the vertical and horizontal dimensions with equal distancescales irrespective of the slope of the sample surface 54. Additionally,the force sensor of this invention is capable of scanning overhorizontal, near vertical, vertical, reentrant and other arbitrarilysloped surfaces 54. This makes scanning possible on complex surfaces 54with curvatures, edges, corners, and undercuts, all of them inthree-dimensional space. The advanced capabilities of the force sensorof this invention make it very suitable for high precision measurementsrequired for metrology applications. In particular the invention isapplicable for critical dimension measurements of semiconductorintegrated circuits.

Multiresonant Oscillators

The key to the functioning of the present invention is the use of amultiresonant oscillator 48 with three separate oscillator resonantmodes that enable force sensitivity in three directions.

The resonant modal shapes and a location of the tip 44 will define thedirections in which the oscillator 48 is sensitive to surface forceinteractions. This establishes the design criteria for the multiresonantoscillator 48.

It is desirable to design an oscillator 48 that has distinct resonantmodes that generate time-varying tip 44 displacement in three orthogonaldirections, making each resonance primarily sensitive in only oneorthogonal direction.

Preferably, the oscillator 48 should have at least three distinctresonant modes, where each resonant mode is ideally sensitive to surfaceforce interactions in only one of the orthogonal directions (maineffect) of the local coordinates 42, and is independent of surface forceinteractions in the other two orthogonal directions (cross-couplingeffect). Some cross-coupling effect can be tolerated. In case of across-coupling effect, a carefully designed experiment can empiricallydetermine the relationship, or cross-coupling, between the resonancesand the surface force interactions in the three orthogonal directions.Furthermore, if the cross-coupling effect is at least an order ofmagnitude less than the main effect, the cross-coupling may beneglected. Otherwise, the feedback control system can and needs tocompensate for cross-coupling effects.

It is desirable that the oscillator resonances have a high quality Qfactor, that will enable detection of resonance shifts in response tosurface force interactions. Failure to detect resonant frequency shiftscan cause loss of control and snapping of the oscillator tip 44 againstthe surface 54.

As shown in FIGS. 8-11, one of the embodiments of this innovationutilizes a simple diving-board shaped oscillator 48. Three resonantmodes that produce three mutually orthogonal vibrations of the tip 44are, for example, the first bending mode, the first torsional mode, andthe second bending mode. The first bending mode generates tip vibrationsin the Z_(tip) direction 46 (FIG. 8) and the first torsional modegenerates tip vibration in the Y_(tip) direction 52 (FIG. 9).Alternatively, a first lateral bending mode of this oscillator can alsobe used to generate tip vibration in the Y_(tip) direction 52. Thesecond bending mode (FIG. 10), can be used to produce tip vibration thatis orthogonal to the tip motion produced by the first bending mode andthe first torsional mode. The second bending mode generates tipvibrations that are primarily in the X_(tip) direction 50, and dependingon the location of the tip 44 also some small tip vibration in theZ_(tip) direction 46. This means that the location of the tip 44 withrespect to the mode shape determines the degree of mode coupling. If onelocates the tip 44 at a node 100 of the mode shape where there is noZ_(tip) 46 displacement, the tip 44 will rock backward and forward alongthe X_(tip) 50 axis, as shown in FIG. 11. However, if one locates thetip 44 at the end of the oscillator 48 where the displacement ismaximum, the tip 44 would experience rocking in the X_(tip) direction 50as well as displacement in the Z_(tip) direction 46. In higher ordermodes it is always possible to find a nodal point 100 that can be usedas a strategic point for location of the tip 44 that will decouple onemodal displacement from another.

In general, different combinations of distinct resonant modes can beused to produce three mutually orthogonal vibrations of the tip 44. Inaddition, the modal shapes of any oscillator 48 can be investigated todetermine a location of the tip 44 where three mutually orthogonal tipvibrations exist.

Naturally, the scanning strategy needs to take advantage of thedirection of displacement of the particular modes to make it sensitivein three distinct directions. For example, for the diving-board shapedoscillator 48 excited in first bending and first torsion, the preferredscanning direction is the Y_(tip) direction 52, laterally with respectto the oscillator 48. Hence, in such an example, a longitudinal scan inthe X_(tip) direction 52 would not make the best use of the directionsof the two resonant modes selected for force sensing.

For more complicated oscillator shapes, the modes selected for forcesensing may be quite different than the ones described in the aboveillustration.

Another embodiment of this innovation utilizes an oscillator 48 with theshape, size, and composition provided in FIG. 12. The probe 48 shown inFIG. 12 is an example of a paddle-shaped oscillator 48 made of singlecrystal silicon. This oscillator 48 can be excited in resonance modessuch as bending, lateral bending, and torsion. In a numericalexperiment, the resonances of the oscillator 48 were as follows: ModeFrequency (Hz) First bending mode 1140 First torsional mode 5509 Secondbending mode 11644 Second torsional mode 40194 Third bending mode 55341Third torsional mode 69500

This is achieved by selecting the shape and the thickness of theoscillator 48. The length-to-width ratio of the oscillator 48contributes to promoting the bending modes. The paddle shape of theoscillator 48 allows excitation of the torsional modes. The thickness ofthe oscillator 48 can be used to insure that the lateral bending doesnot occur before the torsional mode. The relevant resonances aredependent upon the overall dimensions of the oscillator 48 (i.e., itslength, width, and thickness). The resonant frequencies are dependent on√{square root over (k/m)} where k is the modal stiffness and m is themodal mass. Hence, smaller oscillators 48 having less modal mass havehigher resonant frequencies. The oscillator 48 depicted in FIG. 12 mayhave a thickness, t, of approximately 0.15 microns, a width, w, of thepaddle of approximately 110 microns, a length, d, of the paddle of 90microns, and an arm with a width of 20 microns and a length, l, of 140microns. These dimensions are used to illustrate one possible embodimentof a paddle-shaped oscillator 48. However, the present invention neednot be limited to this specific set of dimensions or shapes. Thispaddle-shaped design allows the oscillator 48 to have at least threedistinct resonant modes.

Yet another embodiment of this innovation utilizes an oscillator 48 withthe shape, size, and composition provided in FIG. 13, which is amultiresonant oscillator 48 capable of vertical (Z_(tip)) 46, lateral(Y_(tip)) 52, and longitudinal (X_(tip)) 50 imaging.

So that the resonances will have a high Q, the oscillator 48 may bemanufactured from a single silicon crystal cantilever 48. Otherembodiments may include such materials as silicon nitride or compositelayered material. Furthermore, Q is affected by the quality and surfaceof the oscillator structure 48.

Vibration Sensing System

The function of the vibration sensing system is to transfer the responseof the force sensor into information useful for the feedback controller.The feedback controller drives the scanning probe 48 over the sample 54via a three dimensional actuator system.

The force sensor of this invention can have sensitivity in threeorthogonal directions, in contrast to the conventional force sensor thatis only sensitive to one direction. An embodiment of the presentinvention can use an oscillator 48 that utilizes resonant modes such asbending, second bending, lateral bending, and torsion, to accomplishforce sensing in multiple mutually orthogonal directions. These higherand more complex resonant modes require a greater bandwidth in thevibration sensing system and capability to monitor multiple resonantvibrations simultaneously. The requirement to monitor oscillatorvibrations implies that the signal from the force sensor is an ACsignal.

The vibration sensing system needs to be capable of recording thealteration of the multiple resonances under the influence of the surfaceforce interactions.

In the preferred embodiment of this invention, the vibration sensingsystem is a laser-bounce based sensing system. In this embodiment thereis a focused laser beam pointed towards the oscillator 48 at anoscillator location where there is maximum displacement in all of theresonant modes, and a detector that monitors the displacement of thereflected laser beam. The preferred detector of this invention is acontinuous position sensitive detector (CPSD). A CPSD is capable ofmonitoring the position (DC signal) and displacement (AC signal) of thecentroid of the reflected light beam on the surface of its aperture.Alternatively, one may use a quadrant position sensitive detector(QPSD), commonly used with conventional scanning prove tools, to detectthe position and displacement of the reflected light beam on the surfaceof its aperture. However, QPSDs typically require a focusing lens toform perfectly circular reflected light beam on the aperture of the QPSDdetector.

In another embodiment, other types of vibration sensing system are alsoapplicable, such as, a fiber optic or bulk interferometer, an intensitybased sensor, light-polarization based sensor, a piezoelectric sensor,capacitive sensor, a magnetometer based sensor, and electromagneticradiation based sensors. Any of the sensing systems can be an externalor integrated with the oscillator 48. Other types of vibration sensors,as known to those with ordinary skills in the art, may also be utilized.

In the present innovation, there are three methods that can be used formonitoring the alteration of multiple resonances under the influence ofthe surface force interactions: (1) in the frequency domain, (2) in thespatial domain, and (3) a combination of the other two methods. Thefrequency domain method is the preferred vibration monitoring method ofthis invention.

In the frequency domain, a single broadband output signal from thedetector can be processed with a spectrum analyzer and divided into asmany spectral domains as needed. Each of the spectral domains ofinterest corresponds to each utilized resonant frequency of theoscillator 48. In the preferred embodiment there are three resonantfrequencies of interest. The spectrum analysis can be achieved by notchfiltering the detector output signal so as to only allow the frequencyof interest to be monitored, by fast-fourier-transformation (FFT) of thedetector output signal, and by signal extraction with the help oflock-in amplifiers. Because the modal shape of the oscillator 48determines the direction of the force sensor sensitivity, each frequencyalready has the information about the direction of the sensitivityalready embedded in it. Therefore, the vibration sensing system does nothave the responsibility of determining the directions of sensitivity ofthe force sensor; it only needs to extract information about eachfrequency of interest.

In the preferred embodiment, the output of the vibration sensing systemincludes a vibration amplitude and a phase shift associated with eachfrequency used for force sensing. A feedback controller can use eitheran amplitude change or phase shift information, or a combination of bothto keep the tip at constant surface force interaction levels in allthree directions.

For spatial domain based vibration sensing, each direction of the forcesensor sensitivity is associated with a particular spatial displacementof the oscillator 48 or a combination of spatial displacements. Ingeneral, spatial displacement of the oscillator 48 may be translationalor rotational. The spatial displacements of the oscillator 48 areassociated with a direction sensitive detector system that helpstransform each direction of the force sensor sensitivity with a uniqueoutput that can be used with a feedback controller.

In the preferred laser-bounce based vibration sensing system of thisinvention, the direction sensitive detector is a continuous positionsensitive detector (CPSD) or a system of strategically positioned CPSDsthat help in monitoring the reflected laser beam in spatialdisplacements that can be geometrically transformed into unique outputs.For a valid geometrical transformation it is important that the numberof known CPSD spatial displacements be greater than or equal than thenumber of unknown spatial displacements of the oscillator 48 to beobtained.

FIG. 23 illustrates the spatial domain based method of vibrationsensing. In this illustration the X_(tip) axis 50 of the oscillator 48is perpendicular to the detector aperture (Y_(cpsd) A52-Z_(cpsd)A46),where the Y_(tip) axis 52 of the oscillator 48 is parallel to theY_(cpsd) axis A52 of the detector, and the Z_(tip) axis 46 of theoscillator 48 is parallel to the Z_(cpsd) axis A46 of the detector.

The incident A1 and reflected A2 laser beams are aligned along theX_(tip) axis where the incident laser beam A1 is pointed towards thefree end of the oscillator 48 at an angle and the reflected laser beamA2 is pointing towards the aperture of the detector and away from theoscillator 48. In this configuration, a first bending 108 mode of theoscillator 48 would produce a free-end-of-the-oscillator spatialdisplacement in the Z_(tip) direction 46 and the reflected laser beam A2would produce a trace on the detector aperture that extends in theZ_(cpsd) direction A46. A second bending 109 mode of the oscillator 48would produce free-end-of-the-oscillator spatial displacement mainly inthe X_(tip) direction and the reflected laser beam would produce a traceon the detector aperture that also extends in the Z_(cpsd) directionA46. A geometric transformation can be used to decouple the Z_(cpsd) A46output of the detector to determine the contribution from the first 108and the second 109 bending modes. A first torsion 106 or first lateralbending 107 mode of the oscillator 48 would produce afree-end-of-the-oscillator spatial displacement mainly in the Y_(tip)direction 52 and the reflected laser beam would produce a trace on thedetector aperture that extends in the Y_(cpsd) direction A52. A timedomain sampling of the laser trace on the aperture of the detector willproduce outputs that are associated with the three resonant modes. Ageometrical transformation may be used to produce detector outputs thatare uniquely associated with the three resonant modes. Therefore, wehave obtained three unique detector outputs associated with threeresonant modes of the oscillator 48. Because the modal shape of theoscillator 48 determines the direction of the force sensor sensitivity,we can therefore associate each direction of the force sensorsensitivity with a unique output that can be used with a feedbackcontroller.

The spatial domain based vibration method allows the present inventionto take advantage of multi-dimensional sensing systems, such as thosedisclosed in MANCEVSKI1, that are capable of sensing angulardisplacements and vibrations as well as linear displacements andvibrations.

The multi-dimensional sensing systems described in MANCEVSKI1 alsodisclose an oscillator 48 with a fiducial surface, which is a reflectivecoating at the free end of the oscillator 48 surrounded by anon-reflective surface. When this mirror-on-an-oscillator is illuminatedwith a collimated light beam with an illumination area that is manytimes larger than the area of the fiducial surface, we can observein-plane displacements and vibrations of the oscillator 48. Lateralbending mode 107 qualifies as an in-plane motion. Therefore, theoscillator 48 with fiducial surface disclosed in MANCEVSKI1 is suitablefor monitoring the lateral spatial displacement of the oscillatordisplacements of the tip 44 generated with the lateral bending mode 107.

In the third vibration sensing system method we combine the frequencydomain and spatial domain methods to monitor the vibration signals ofthe resonating oscillator 48.

It is required that all relevant components of the vibration sensingsystem, such as the continuous position sensitive detector (CPSD), theassociated electronics, the data acquisition, and the control systemaccommodate the frequency bands of the oscillator resonances. Thebandwidth of a typical CPSD sensor disclosed in MANCEVSKI1 is in the MHzregion. This frequency band is more than sufficient to be used with mostcommercially available oscillators 48. Currently, commercially availablePC based data acquisition and control system, such as one from NationalInstruments, has a bandwidth of 100 KHz for a single channel. A moreadvanced data acquisition and control system from National Instrumentshas a bandwidth of 333 to 500 KHz, depending on the digital bitresolution. Those bandwidths are sufficient for implementation ofreal-time feedback control. However, the present invention need not belimited to this specific PC-based data acquisition and control system.Any data acquisition and control system known to those skilled in theart may be utilized in other embodiments of the present invention.

In one embodiment of the invention, the output signal from the CPSD isdirectly digitized with the help of data acquisition hardware. With thisapproach, the spectral analysis of the signal and the feedbackcontroller may all be done digitally in software. The advantage of thisdigital approach is its flexibility to handle complex logic operationsand sophisticated feedback controllers, and the elimination of expensiveanalog instruments such as lock-in amplifiers.

In another embodiment of the present invention the laser intensity ofthe laser-bounce based vibration sensing system may be time varyinginstead of being constant. In one embodiment, the frequency of the laserintensity variation may coincide with one or more of the resonantfrequencies of the oscillator 48. In another embodiment, the frequencyof the laser intensity variation may be different than the resonantfrequencies of the oscillator 48.

Excitation System

The invention also incorporates an excitation system that is used toexcite the oscillator resonances used for force sensing. The excitationsystem of the preferred embodiment uses a piezoelectric (PZT) diskactuator 102 mounted next to the oscillator base 104 to providemechanical energy to the oscillator 48. The PZT disk actuator 102 isexcited with a signal that is an algebraic sum of signals withfrequencies equal or close to the resonant frequencies of the oscillator48. The excitation signal can excite only the frequencies of interestand not the other resonant frequencies. The excitation signal can bealso used as a reference signal for the spectrum analysis of thedetector output signal. Other types of oscillator excitation mechanisminclude electrostatic, magnetic, and thermal.

Feedback Control

In principle, an embodiment of the present invention operates bypositioning a resonating oscillator 48 with three resonant modes withrespect to a three-dimensional surface 54. Positioning the tip 44 of theoscillator 48 in proximity to the surface 54 alters the excited resonantfrequencies of the oscillator 48. The magnitude of the resonancealteration will depend on the actual distance 112 between the tip 44 andthe sample 54 and the orientation between the oscillator 48 and thesample 54.

In one embodiment of the present invention the tip-sample distance 112is controlled by a three-dimensional mechanical actuator. Thisthree-dimensional mechanical actuator moves the tip 44 to a desireddistance 112 from the sample surface 54 and in directions consistentwith the functioning of the multi-directional force sensor. The tip 44of the oscillator 48 vibrates with a small amplitude in threeperpendicular directions (X_(tip) 50, Y_(tip) 52, Z_(tip) 46). In theproximity to a sample surface 54, when the tip 44 is in the attractiveatomic force region, a resonant frequency of the oscillator 48 willdecrease, and when the tip 44 crosses into a repulsive atomic forceregion, the resonant frequency of the oscillator 44 will increase. Afeedback loop uses these resonance shifts to keep the tip at a constantsurface force interaction level in all three directions.

Several methods can be used to implement the feedback controller. In onemethod there are three independent PID(proportional-integrated-derivative) controllers, one for each forcesensing direction, that operate independently of each other and in asimultaneous manner. These are called three single-input single-output(SISO) controllers. In this method, each controller is not aware of theoperation of the other two controllers and any feedback action by thetwo other controllers will be seen as a disturbance to the thirdcontroller. This method works the best when all three resonances areuncoupled and independent. After the feedback controllers produce anoutput, it is possible to transform the three outputs into another threeoutputs to satisfy the coordinate system of the actuator.

In a variation of the SISO controller, each PID controller may beemployed one at a time, where some switching logic is implemented toswitch from one controller to another. The switching logic needs to beable to determine when the surface 54 changes direction (e.g., anincoming vertical wall A10 after a flat horizontal surface A11). Tosatisfy this requirement, one of the resonances that does notparticipate in the active controlling (for example resonance A106 thatcorresponds to mode 106) may be used as a monitor of an incoming surfaceA10 in the direction in which it is primarily sensitive. After the tip44 reaches a certain critical point, the PID controllers will becommanded to switch. After such a switch, a resonance that was used formonitoring (for example resonance A108 that corresponds to mode 108)becomes the primary controlling instrument and the former controllingresonance A106 becomes a monitoring resonance.

In another method, there are three dependent PID controllers, one foreach force sensing direction, that operate coupled with each other andin a simultaneous manner. This implementation uses one multiple-inputmultiple-output (MIMO) controller. In this method, the column vector ofthe three inputs from the vibration sensing system is multiplied by amatrix of input-output co-dependencies to produce the actuator outputcolumn vector. The matrix represents the cross coupling between thesurface force interactions and the resonance alterations associated withthe three resonant modes A108, A106, and A109. If there is no crosscoupling then the respective off-diagonal matrix elements are zero. Fora fully decoupled system the matrix is a diagonal matrix. Thecoefficients of the matrix may be determined by modeling the forcesensor or may be obtained experimentally. For example, one couldexperimentally observe alterations in resonant frequencies as theoscillator 48 is displaced towards a surface 54 in the X Y and Zdirections, respectively.

In a variation of the MIMO controller, there may be more than threeinputs, each associated with an oscillator resonance. Utilizing morethan three resonances can improve the confidence level associated withthe force sensing. Each of the extra resonances needs to be sensitive tothe resultant of the surface force interaction in a particulardirection. If an extra resonance is sensitive in more than onedirection, the contribution of each surface force interaction of aparticular direction to that resonance needs to be known. For example, asecond bending mode 109 of a preferred oscillator 48 is mainly sensitiveto the resultant surface force interaction in the X_(tip) direction 50and is somewhat sensitive to the resultant surface force interaction inthe Z_(tip) direction 46. The outputs of this MIMO controller are threeactuator signals proportional to the three perpendicular force sensingdirections, where each controller output is a result of the contributionof many resonances.

In a variation of the above MIMO controller, a neural network may beemployed to automatically weight the contribution of each surface forceinteraction of a particular direction to each resonance monitored.Neural networks can increase the confidence associated with the forcesensing.

A controller, using any of several different types of control logic, canbe used to command actuators to move either the tip 44 or the sample 54relative to each other in response to sensed alterations in the naturalfrequencies of multiple resonances, as shown in FIG. 15. X_(tip) 50 andglobal X axis point out of the paper of FIG. 15 at the reader.Therefore, the YZ plane is the parallel with the surface of the paper ofFIG. 15. One such type of control logic is to maintain either theamplitudes 114 or the frequency differences 110 (expressed through phasedifferences) of the respective resonances at fixed predeterminedset-point values, in all three directions. Each direction may have adifferent set-point. Alternatively, the control logic may include analgorithm for adjusting the amplitude 114 or phase-shift 110 set pointsassociated with the respective resonances during the scan. The amplitude114 or phase-shift 110 set points can be adjusted either continuously orin discrete steps during the scan. Adjustments of the amplitude 114 orphase-shift 110 set points can be based on an empirically determinedcontrol law. Alternatively, adjustments of the amplitude 114 orphase-shift 110 set points can be determined adaptively so as to causethe apex 45 of the tip 44 to move substantially parallel to the samplesurface 54 during the scan. Such adaptive adjustments of the amplitude114 or phase-shift 110 set points require determination and use of aforce calibration curve for each of the respective modal resonances usedfor force sensing. Such force calibration curves relate either theamplitude 114 or phase shift 110 of the respective resonance to thetip-surface distance 112.

Improved Scan Control

In one embodiment, the force sensor can be used to provide additionalinformation useful for improved scan control by building a nearreal-time estimate of the three-dimensional orientation of the region ofthe sample surface momentarily in proximity to the tip 44. This methodrequires determination and use of a force calibration curve for each ofthe respective modal oscillations used for force sensing. Such forcecalibration curves relate either the amplitude 114 or phase shift 110 ofthe respective oscillation to the tip-surface distance 112. Surfaceforce interaction vectors along the respective local coordinate axes 42can be determined once such calibration curves are known. The estimatedorientation of a sample surface region in proximity to the tip 44 isestimated as normal with respect to the vector F′ 82 shown in FIGS. 3Band 3C (i.e., the sum of the three surface force interaction vectors).This normal assumption is valid for the special case of an infinitehomogenous plane sample surface. Other variations of the control logiccan be used to take into account the integrated effects associated witha finite, non-planar sample surface 54. To accomplish improved scancontrol, the apex 45 of the tip 44 is commanded to move substantiallyparallel to the estimated sample surface 54 during the scan. This methodhelps prevent crashing the tip 44 when an abrupt increase of surface 54slope is encountered (e.g., encountering a vertical wall). This methodalso helps prevent the tip surface distance 112 from increasing too muchwhen an abrupt decrease in surface 54 slope is encountered (e.g.,encountering the edge of a feature).

In another embodiment, an improved estimate of sample 54 topography canbe obtained by post processing the data recorded during a previous scan.Approximate sample topography obtained from the first scan is used toestimate the vector field F′ 82 representing the surface forceinteractions in the region near the sample surface 54 traversed by thetip 44 during the scan. The scan data is then reprocessed using this newestimate of the vector field F′82, resulting in improved estimate of thesample 54 topography. The post processing procedure can be repeatedmultiple times until differences in estimated surface 54 topography arearbitrarily small. This method allows integrated effects from thesurface 54 on the tip 44 to be taken into account. Integrated effectsare the cumulative effect of forces from a relevant volume of the sample54 acting on the tip 44.

Other logic systems may be employed to gather data. For example, onecould record a historical surface interaction field F′ 82 based on anSPM tip 44 positioned by the XYZ stage. By retracing the prior motion ofSPM tip 44, one can compare the present surface 54 interaction field toa historical profile. This can be done to verify the repeatability andreliability of scans generated using the present invention. Furthermore,such verifications can be done to provide a quality assurance check onsurfaces 54 requiring specific profiles. Another embodiment may use thistype of comparison to detect changes or flaws of the surface 54.

In yet another embodiment, repeated sampling of a known sample 54 allowsthe accuracy of the present invention to be improved by tracking therepeatability of the system on a known sample 54. By sampling a knownsurface 54, a new SPM tip 44 can be calibrated by developing acorrection factor or matrix that matches the obtained result to theexpected result.

In still another embodiment of the present invention, shown in FIG. 24,the tip 44 can be made to scan longitudinally A5 along narrow featuressuch as metal interconnect lines or resist lines 54 used on themanufacture of semiconductors, instead of laterally with respect to suchfeatures. The ability of the present invention to sense a component ofthe tip-sample interaction force vector 82 in the X direction enablessuch a longitudinal scan. Advantages of scanning such featureslongitudinally include improved scanning speed and improved ability tomeasure sidewall roughness.

Tilted Probe

In a preferred embodiment of the invention, the oscillator 48 can betilted around the long axis 116 of the oscillator 48, as shown in FIG.16. Preferably, the oscillator 48 tilt angle A115 is larger than thehalf-cone angle of the tip 44 as to allow the apex 45 of the tip 44 toreach vertical and reentrant sidewall surfaces on the sample 54, asillustrated in FIG. 17. The maximum tilt angle A115 is limited by thewidth of the oscillator 48 at its free end and the spacing of twosidewall surfaces 54 between which the tip 44 may need to be inserted.For the present invention the typical tilt angle A115 is between 6 and20 degrees, but is not limited to this range. In this embodiment, thepreferred scan direction is in the Y direction, or laterally withrespect to the oscillator 48. For such a tilted probe, the verticaltip-sample force vector 82 associated with a horizontal sample surfaceAll will couple to both the bending 108 and torsional 106 modes of theoscillator 48, as shown in FIG. 15. Additionally, a horizontaltip-sample force vector 82 associated with a vertical sample surfaceA10, will also couple to both the bending 108 and torsional 106 modes ofthe oscillator, as shown in FIG. 15. Therefore, there will be twosurface force components that can be detected by the tilted resonatingoscillator 48 in all of its possible angular orientations. Theirmagnitude will depend on the orientation of the probe tip 44 withrespect to the surface 54. An experimentally obtained scan of a line ina semiconductor integrated circuit with the tilted probe system isrepresented in FIG. 18. In this scan, the tip 44 was first tilted in onedirection, and afterwards in the other. The image 120 is a patch of theimages obtained in the left and right scans.

Carbon Nanotube Tips

Advanced semiconductor integrated circuit features with high aspectratios are hard to inspect with conventional scanning probe tools thatcannot reach vertical, near vertical, or inverted sidewalls A120. Thisproblem is well known to those of ordinary skills in the art. Using anembodiment of the present invention with a tilted probe addresses thisproblem.

Another problem with conventional scanning probe tools is thatconventional silicon tips 44 have a hard time accessing the bottoms ofhigh aspect ratio trenches of advanced semiconductor integrated circuitfeatures. This problem is well known to those of ordinary skill in theart. Conventional silicon tips 44 typically have a half-cone angle of 20to 30 degrees and are often an integral part of the silicon oscillator48 structure. An embodiment of the present invention with a tilted probealso has to deal with the feature access problem.

Therefore, to measure line-widths and trench-widths with high aspectratios encountered with advanced semiconductor integrated circuitfeatures, it is desirable to have a very sharp tip 44 that can reachwithin the trench bottom and along vertical or reentrant sidewalls A120.

The left sidewall 119 has an angle of 85.8° (57 nm undercut). The rightsidewall 121 has an angle of 88.5° (20 nm undercut).

In an embodiment of the present invention, the standard oscillator tip44 is extended with an aligned nanotube tip 124 grown from the apex ofthe sharp SPM tip 44 using one of the methods described in MANCEVSKI2,as shown in FIG. 19. Preferably, the nanotube 124 is carbon. It isdesirable to have a very sharp tip 44 as a support structure on which acarbon nanotube tip extension 124 is grown. Preferably, the sharp tip 44has a half-cone angle of 3 to 6 degrees.

In another embodiment of the present invention, the support structure onwhich a carbon nanotube tip extension 124 is grown is a columnstructure, as depicted in FIG. 20. The column support structure 44 isattached to an oscillator 48 or cantilever 48 as a SPM tip 44 and may bean integral part of the probe structure. The present invention is notlimited to this type of support structure 44. A nanotube tip extension124 or multiple nanotube tip extensions 124 can be grown from thesupport 44. Nanotubes 124 can be grown in accordance with the teachingof MANCEVSKI2. Carbon nanotube tip extensions 124 that are simplyattached or glued are less rigid, less stable, and provide less controlover the position and orientation of the carbon nanotube tip extension124, than ones that are grown in place using one of the methodsdescribed in MACEVSKI2.

A nanotube 124 or multiple nanotubes 124 may be oriented in anydirection relative to the structure 44. As an example, FIG. 20illustrates nanotubes 124 oriented in lateral and vertical directions,which enable enhanced imaging of vertical and near vertical sidewallsA120 and trench bottoms with a same nanotube tip extension 124. The fivenanotube tip extensions 124 shown in FIG. 20 are each perpendicular toone another. Hence, two nanotube tip extensions 124 extend along theX_(tip) axis 50, two nanotube tip extensions 124 extend along theY_(tip) axis 52, and one 124 extends along the Z_(tip) axis 46.

Carbon Nanotube Oscillators

In yet another embodiment of the present invention, the tip 44 is nolonger a static rigid body that is used to transmit a tip-sample forceinteraction 82 to the elastic body of the oscillator 48, but it 44participates in the dynamics of the force sensing. In this embodiment,the tip 44 is also an elastic body that is capable of oscillating in oneor more resonant modes, as shown in FIG. 21. Preferably, the elastic tip44 is a nanotube 126, or more specifically a carbon nanotube 126. Wewill refer to such an elastic nanotube tip 126 as a “nanotubeoscillator” 126. Hence, the function of a nanotube oscillator 126 is toserve as a force sensor. Preferably, a nanotube oscillator 126 is madefrom or at least comprises carbon.

Multiple resonant modes of a nanotube oscillator 126 can be used toprovide sensitivity in at least one and preferably all three directions(X_(tip) 50, Y_(tip) 52, Z_(tip) 46) of the tip-sample force interaction82. The nanotube oscillator force sensor embodiment of the presentinvention is consistent with all the capabilities and functions of theoscillator force sensor embodiment of our invention, and all discussionsof the oscillator force sensor (characteristics, control, sensing, use,etc.) apply to the nanotube oscillator force sensor.

In a preferred nanotube oscillator force sensor embodiment of thepresent invention there is a column support structure 48 verticallyoriented with respect to the global coordinate system 40 of the sample.Another type of support structure 48 for the nanotube oscillator may bea rigid sharp tip 44. In the preferred embodiment there is a singlecarbon nanotube 126 oriented vertically, as shown in FIG. 21. Oneresonance of interest is the second bending mode 109 that will produceend-of-nanotube vibration that is vertical and therefore sensitive tothe vertical Z component 74 of the surface force vector 82. Thisresonant mode may have a projection in the XY plane that is in anydirection. However, this is not relevant because the distal end of thenanotube oscillator 126 will move up and down in the vertical direction(Z) irrespective of the orientation of this mode.

Another resonance that can be used for force sensing is the firstbending mode 108 of the nanotube oscillator 126. Because the nanotube126 is a molecularly perfect cylindrical structure, there will be twofirst bending modes that have identical frequencies but produceend-of-nanotube vibrations that are normal to each other. Depending onthe phase of the two bending resonant frequencies the end-of-nanotubevibration may be a diagonal or circular motion. Those two resonances aresensitive to the X and Y directions of the surface force interaction 82,respectively. Although the resonant frequencies of the two modes are thesame, they can be separated by their phase and therefore made useful fora feedback control, i.e., sensitive to the X and Y directions of thesurface force interaction 82. In one of the embodiments of thisinvention, the phase of the two identical frequencies is influenced tobe different by controlling the initial condition of the excitation. Inanother embodiment of this invention, a magnetic particle 128 isattached at the end of the nanotube 126 to destroy the symmetry andproduce distinguishing resonances with separated modes, as shown in FIG.22. The magnetic particle 128 may also be used to magnetically excitethe nanotube oscillator 126. In another embodiment of this invention(not shown) the grown nanotube has a shape that is not symmetrical toproduce distinguishing resonances with separated modes.

Means of exciting a nanotube oscillator 126 include (but are not limitedto):

-   1) magnetic coupling to a magnetic particle 128 attached at the    distal end of the nanotube oscillator 126,-   2) coupling of electromagnetic radiation energy to the nanotube    oscillator 126,-   3) electrostatic coupling to a charged particle attached at the    distal end of the nanotube oscillator 126,-   4) thermal gradient near the nanotube oscillator 126,-   5) piezoelectric element 102 coupled to the support structure 48 or    the support structure 48 may be a piezoelectric element 102, or-   6) combination of any of the above means of excitation. Means of    detecting the vibrations of a nanotube oscillator 126 include (but    are not limited to):-   1) magnetic coupling to a magnetic particle 128 attached at the    distal end of the nanotube oscillator 126,-   2) current readout from the nanotube oscillator 126 that has been    exposed to electromagnetic radiation or a stress,-   3) inductive pick-up coil and corresponding tank circuit,-   4) capacitive readout element positioned next to the nanotube    oscillator 126 having a charged particle attached at its distal end,-   5) an optical beam illumination and detection of its scattering, or-   6) combination of any of the above means of detection.

In another embodiment of the nanotube oscillator force sensor embodimentof the present invention, there is a column support structure 48vertically oriented with respect to the global coordinate system 40 ofthe sample. In this embodiment there is more than one carbon nanotube126, as depicted in FIG. 20, where each nanotube oscillator 126 isresponsible for detecting the component of the surface force vector 82in the direction in which it extends. Therefore, the vertically orientednanotube oscillator 126 is sensitive to vertical direction of thesurface force interaction, and the horizontally (in X and Y) orientednanotube oscillators 126 are sensitive to the horizontal (X and Y)directions of the surface force interaction 82. In this embodiment it issufficient that each nanotube oscillator 126 utilize only one of itsresonances because its orientation determines the direction of itssensitivity. Preferably, the single resonance of each nanotubeoscillator 126 is the second bending mode 109 that will produceend-of-nanotube vibration that is oriented along its length andtherefore it is sensitive to the direction of the surface forceinteraction 82 that is oriented along the length of the nanotube 126.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this invention provides a system and method ofmulti-dimensional force sensing for scanning probe microscopy. Althoughjust a few embodiments of the present invention have been described indetail herein, it should be understood that the drawings and detaileddescription herein are to be regarded in an illustrative rather than arestrictive manner, and are not intended to limit the invention to theparticular forms and examples disclosed. On the contrary, the inventionincludes any further modifications, changes, rearrangements,substitutions, alternatives, design choices, and embodiments apparent tothose of ordinary skill in the art, without departing from the spiritand scope of this invention, as defined by the following claims. Thus,it is intended that the following claims be interpreted to embrace allsuch further modifications, changes, rearrangements, substitutions,alternatives, design choices, and embodiments.

1-82. (canceled)
 83. A device, comprising: a support structure; at leastone nanotube extending from the support structure; and an excitationsystem operable to vibrate the nanotube.
 84. A device in accordance withclaim 83, wherein the nanotube is excited to at least one resonantfrequency.
 85. A device in accordance with claim 83, wherein thenanotube comprises carbon.
 86. A device in accordance with claim 83,wherein the excitation system comprises a coil.
 87. A device inaccordance with claim 86, wherein the coil operates to couple anelectromagnetic field to the nanotube.
 88. A device in accordance withclaim 83, wherein the excitation system comprises an antenna.
 89. Adevice in accordance with claim 83,. wherein the excitation systemcomprises a piezoelectric element.
 90. A device in accordance with claim89, wherein the piezoelectric element operates to couple mechanicalenergy to the nanotube.
 91. A device in accordance with claim 83,wherein the excitation system comprises a capacitive element.
 92. Adevice in accordance with claim 91, wherein the capacitive elementoperates to couple an electrostatic field to the nanotube.
 93. A device,comprising: a support structure; at least one nanotube extending fromthe support structure, wherein the nanotube has a free end opposite theattachment to the support structure; a magnetic element coupled to thenanotube near the free end of the nanotube; and an excitation systemoperable to excite the nanotube to at least one resonant frequency. 94.A device in accordance with claim 93, wherein the excitation systemcomprises a coil.
 95. A device in accordance with claim 94, wherein theexcitation system comprises a tank circuit.
 96. A device in accordancewith claim 94, wherein the coil operates to couple an electromagneticfield to the magnetic element.
 97. A device, comprising: a supportstructure; at least one nanotube extending from the support structure,wherein the nanotube is electrically charged; an excitation systemoperable to excite the electrically charged nanotube to at least oneresonant frequency
 98. A device in accordance with claim 97, wherein theexcitation system comprises a capacitive element.
 99. A device inaccordance with claim 98, wherein the capacitive element operates tocouple an electrostatic field to the charged nanotube.
 100. A device,comprising: a support structure; at lest one nanotube grown directlyonto and extending from the support structure; and an excitation systemoperable to vibrate the nanotube.